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<span class="kw">consider </span><font color="Maroon" title="c3">g</font> being  <a href="funct_1.html#V3" title="FUNCT_1:attr.3">V8</a>() <a href="hahnban1.html#NM2" title="HAHNBAN1:NM.2">linear-Functional</a> of <font color="Maroon" title="c2">V</font>;<br/>
<a NAME="E2:61_1_1"/><span class="lab"><font color="Green" title="E32">A1</font></span>: 
<font color="Maroon" title="c3">g</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="hahnban1.html#K7" title="HAHNBAN1:func.7">0Functional</a> <font color="Maroon" title="c2">V</font>
 
;<br/>
<span class="kw">reconsider </span><font color="Maroon" title="c4">g</font> = <font color="Maroon" title="c3">g</font> as   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <span class="p1">(<span class="default"><font color="Maroon" title="c2">V</font> <a href="hahnban1.html#K8" title="HAHNBAN1:func.8">*'</a> </span>)</span> <span class="kw">by</span> <span class="lab"><a class="ref" href="hahnban1.html#D14" title="HAHNBAN1:def.14">HAHNBAN1:def 14</a></span>;<br/>
<span class="kw">assume </span><a NAME="E4:61_1_1"/>
<font color="Maroon" title="c2">V</font> <a href="hahnban1.html#K8" title="HAHNBAN1:func.8">*'</a>  is  <a href="struct_0.html#V7" title="STRUCT_0:attr.7">trivial</a> 
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> contradiction</span><br/>

<a NAME="E5:61_1_1"/><span class="kw">then </span>
<font color="Maroon" title="c4">g</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="struct_0.html#K4" title="STRUCT_0:func.4">0.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">V</font> <a href="hahnban1.html#K8" title="HAHNBAN1:func.8">*'</a> </span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="struct_0.html#D19" title="STRUCT_0:def.19">STRUCT_0:def 19</a></span>;<br/>
<span class="kw">hence </span><a NAME="E6:61_1_1"/>
contradiction
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:61_1_1"><span class="lab"><font color="Green" title="E32">A1</font></span></a>, <a class="ref" href="hahnban1.html#D14" title="HAHNBAN1:def.14">HAHNBAN1:def 14</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


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